Time-Varying Hurst Exponent And Multiferactal Analysis For China Stock Market

In this paper, the dynamical behavior of the China stock markets is characterized on the basis of the temporal variations of the Hurst exponent estimated with detrended fluctuation analysis over moving windows for the historical Shanghai Composite Index and Shenzhen Component Index daily return, volatility and exchange quantity. According to the results drawn:(1)Shanghai Composite Index and Shenzhen Component Index daily return and volatility have persistence, volatility has stronger long memory than return, but exchange quantity has Anti-persistence.(2)Shanghai Composite Index has weaker long-term memory than Shenzhen Component Index, show Shanghai stock market more effective than Shenzhen stock market.(3)The time varying Hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior, the time varying Hurst exponent manifests cyclic, non-periodic dynamics. This means that the market exhibits a time-varying short-term inefficient behavior that becomes efficient in the long term. Time-varying Hurst for return and volatility presence of a dominant cycle with a period of 8 years, but time-varying Hurst for exchange quantity presence of a dominant cycle with a period of 4 years.Hurst exponent can only described time series fluctuations in the macro outlook, while the multifractal structure can describe time series locally and more detailed analysis. We investigate the multifractal properties of the returns and volatility of the China financial indices by applying the multifractal detrended fluctuation analysis. The research results show:(1)Returns and volatility possess multifractality, the generalized Hurst exponent obviously depends on the order of fluctuate function and change with it; the curve of scaling function clearly departs from a straight line, shows nonlinear property; the multifractal spectrum displays the commonly observed bell shape.(2)Through shuffling procedure and phase randomization procedure, the original time series and the transformed time series are compared. It is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and nonlinear temporal correlations. Most multifractality of the data is due to fat-tailed probability distributions, but the different long range correlations for small and large fluctuations also contribute to the multifractal behavior of the time series.(3)Large fluctuations have higher contributions to the multifractality degree than those corresponding to small fluctuation. This reinforces the hypothesis that small and large fluctuations are due to different dynamic mechanisms. Shenzhen Stock market has stronger multifractality than Shanghai Stock market, the multifractality degree of price and volatility returns are similar. On the other hand, volatility returns have stronger evidence of long-range dependence than price returns. Thus, we deduce that strong long-range correlations do not enhance the multifractality.To sum up, China stock market price behavior exists a positive feedback mechanism. Investor's investment activities are inter-related and investor sentiment interaction affect the stock price behavior can not be ignored.Price behavior demonstrated long-term memory characteristics, today's prices would have an impact on the future price. The time-varying Hurst index describe the Chinese stock market long-memorty nature.This feature may be due to changes in the market over time, the creation of new financial products, as well as changes in investors has led to changes in market microstructure. According to the time-varying Hurst index with the average non-periodic cycle, the Investors should take advantage of the complex technical analysis tools such as price series with 8 years cycle, volume series with 4 years cycle, long-memory of sequence, multi-fractal characteristics to obtain short-term price trends, then to predict the stock market.